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          电路分析基础(上册 )
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        <h1 id="电路分析基础-上册"><a href="#电路分析基础-上册" class="headerlink" title="电路分析基础(上册 )"></a>电路分析基础(上册 )</h1><span id="more"></span>
<h2 id="第一篇-电阻电路的分析"><a href="#第一篇-电阻电路的分析" class="headerlink" title="第一篇    电阻电路的分析"></a>第一篇    电阻电路的分析</h2><h3 id="第一章电压，电流约束关系"><a href="#第一章电压，电流约束关系" class="headerlink" title="第一章电压，电流约束关系"></a>第一章电压，电流约束关系</h3><h4 id="1-方向-P-8"><a href="#1-方向-P-8" class="headerlink" title="1.  方向 P_8"></a>1.  方向 <em>P_8</em></h4><ul>
<li>元件电流参考方向和电压方向常关联。电流方向也就是电压参考“+”级到“—”级方向<ul>
<li><img src="https://gitee.com/xqyr/img/raw/img/image-20220927140136463.png" alt="电路方向" style="zoom:50%;"></li>
</ul>
</li>
</ul>
<h4 id="2-基尔霍夫-P-12"><a href="#2-基尔霍夫-P-12" class="headerlink" title="2. 基尔霍夫 P_12"></a>2. 基尔霍夫 <em>P_12</em></h4><ul>
<li><p>将二端元件视为一条<strong>支路</strong>。流经元件的电流和元件的端电压便分别称之为<strong>支路电流和支路电压</strong>。</p>
</li>
<li><p>电荷守恒的意思是：电荷既不能创造也不能消灭。由此可得基尔霍夫电流定律(Kirchhoff’s current law),该定律简写为KCL。KCL表达了电路中支路电流间的约束(constraint)关系</p>
</li>
<li><script type="math/tex; mode=display">
\sum_{k=1}^K i_k (t) = 0</script></li>
</ul>
<ul>
<li><p>对于任，集总电路中的任，回路，在任，时刻，沿着该回路的所有支路电压降得代数和为零</p>
</li>
<li><script type="math/tex; mode=display">
\sum_{k=1}^K u_k(t)=0</script></li>
</ul>
<h4 id="3-电阻元件-p-20"><a href="#3-电阻元件-p-20" class="headerlink" title="3. 电阻元件 p_20"></a>3. 电阻元件 <em>p_20</em></h4><ul>
<li>电导用G表示，单位 <em>西</em>（符号 <em>S</em>)<script type="math/tex; mode=display">
G= \frac1R</script></li>
</ul>
<h4 id="4-双口元件-——受控源-p-34"><a href="#4-双口元件-——受控源-p-34" class="headerlink" title="4. 双口元件 ——受控源 p_34"></a>4. 双口元件 ——受控源 <em>p_34</em></h4><ul>
<li>受控源是一种<u>双口</u>元件，它含有两条支路，其一为<strong>控制支路</strong>，这条支路或为开路或为短路，另一为<strong>受控支路</strong>，这条支路或用一个受控“电压源”表明该支路的电压受控制的性质或用一个受控“电流源”表明该支路的电流受控制的性质。</li>
</ul>
<div class="table-container">
<table>
<thead>
<tr>
<th><img src="https://gitee.com/xqyr/img/raw/img/20220927143418.png" alt="（电）压控（制）电压源(VCVS)" style="zoom:75%;"></th>
<th><img src="https://gitee.com/xqyr/img/raw/img/20220927143544.png" alt="电流控电压源 CCVS" style="zoom:75%;"></th>
</tr>
</thead>
<tbody>
<tr>
<td><img src="https://gitee.com/xqyr/img/raw/img/20220927143902.png" alt="（电）压控（制）电流源(VCCS)" style="zoom:75%;"></td>
<td><img src="https://gitee.com/xqyr/img/raw/img/20220927144040.png" alt="（电）流控（制）电流源（CCCS)" style="zoom:75%;"></td>
</tr>
</tbody>
</table>
</div>
<h4 id="5-两类约束的独立性-p-44"><a href="#5-两类约束的独立性-p-44" class="headerlink" title="5. 两类约束的独立性 p_44"></a>5. 两类约束的独立性 <em>p_44</em></h4><ol>
<li><p>设电路的节点数为n,则独立的KCL方程为(n-1)个，且为任意(n-1)个。</p>
</li>
<li><p>给定一平面电路(planar circuit):<br>(a)该电路有[b - (n-1)]个网孔；<br>(b)[b-(n-1))]个网孔的KVL方程是独立的。</p>
</li>
</ol>
<h3 id="第二章-网孔和节点法-p-62"><a href="#第二章-网孔和节点法-p-62" class="headerlink" title="第二章 网孔和节点法  p_62"></a>第二章 网孔和节点法  <em>p_62</em></h3><h4 id="网孔法-p-62"><a href="#网孔法-p-62" class="headerlink" title="网孔法 p_62"></a>网孔法 <em>p_62</em></h4><ul>
<li><p>网孔分析是以网孔电流(mesh current)作为第-步求解的对象。所谓网孔电流是一种沿着网孔边界流动的假想电流</p>
<p><img src="https://gitee.com/xqyr/img/raw/img/20220927145203.png" alt="网孔电流" style="zoom:67%;"></p>
</li>
</ul>
<script type="math/tex; mode=display">
\begin{matrix}
&\begin {cases}R_1 i_{M1} + R_5 i_{M1} + R_5 i_{M2} + R_4 i_{M1} - R_4i_{M3} + u_{s4} -u_{s1} = 0 \\
R_{2}i_{M1}+R_{5}i_{M2}+R_{5}i_{M1}+R_{6}i_{M2}+R_{6}i_{M3}-u_{s2} = 0\\
R_{3}i_{M3}+R_{4}i_{M3}-R_{4}i_{M1}+R_{6}i_{M3}+R_{6}i_{M2}-u_{s4}-u_{s3}=0\\\end{cases}
\\&\quad\ 整理得：\\
&\begin {cases}(R_{1}+R_{4}+R_{5})i_{M1}+R_{5}i_{M2}-R_{4}i_{M3}=u_{s1}-u_{S4}\\
R_{5}i_{M1}+(R_{2}+R_{5}+R_{6})i_{M2}+R_{6}i_{M3}=u_{S2}\\
R_{4}i_{Ml}+R_{b}i_{M2}+(R_{3}+R_{4}+R_{6})i_{3M3}=u_{s3}+u_{s4}\\\end{cases}\end{matrix}</script><p>​    <strong>概括为：</strong></p>
<p>​    </p>
<script type="math/tex; mode=display">
\begin{cases}R_{11}i_{M1}+R_{12}i_{M2}+R_{11}i_{M3}=u_{s11}\\ R_{21}i_{M1}+R_{22}i_{M2}+R_{23}i_{M3}=u_{s22}\\ R_{31}i_{M1}+R_{12}i_{M2}+R_{33}i_{M3}=u_{s33}\\ \end{cases}
\begin {matrix}\quad\quad \mathsf{其中R_{11},R_{22},R_{33}风别称为网孔1，网孔2，网孔3的自电阻}\\
\mathsf {他们分别是各自网孔内所有电阻的和}\\
\mathsf {R_{12}为互电阻，他们是该两网孔的公有电阻}\\
\mathsf {u_{s1}为网孔1中各电压源电压升的和。u_{s11}= u_{s1} - u_{s4}}\end {matrix}</script><h4 id="节点分析-p-72"><a href="#节点分析-p-72" class="headerlink" title="节点分析 p_72"></a>节点分析 <em>p_72</em></h4><p><img src="https://gitee.com/xqyr/img/raw/img/20220927154530.png" alt="节点分析法"></p>
<p>概括形式</p>
<script type="math/tex; mode=display">
{\begin {cases}G_{11}u_{n1}+G_{12}u_{m2}+G_{11}u_{31}=i_{s11}\\ G_{21}u_{11}+G_{22}u_{22}+G_{21}u_{33}=i_{22}\\ G_{31}u_{m1}+G_{32}u_{22}+G_{33}u_{33}=i_{33}\\\end {cases}}
\quad\begin {matrix}  G11 为节点1的自电导。是节点1上所有电导的总和，G_{11} = G_1+G_5\\
 G12是节点1和节点2公有电导的负值，G_{12} = -G_1\\
 i_{s11}为电流源输送给节点1的代数和。i_{s11}=i_s \quad i_{s22} = 0\end {matrix}</script><h3 id="第三章-叠加方法与网络函数-p-90"><a href="#第三章-叠加方法与网络函数-p-90" class="headerlink" title="第三章 叠加方法与网络函数 p_90"></a>第三章 叠加方法与网络函数 <em>p_90</em></h3><h4 id="激励与响应"><a href="#激励与响应" class="headerlink" title="激励与响应"></a>激励与响应</h4><ul>
<li><p>由线牲元件及独立电源组成的电路为线性电路。独立电源是电路的输入，对电路起着激励(excitation)的作用。</p>
</li>
<li><p>响应与激励之间存在着<strong>线性关系</strong>。</p>
</li>
<li><p>对单一激励的线性、时不变电路，指定的响应对激励之比定义为<em>网络函数</em>，记为H,即</p>
<script type="math/tex; mode=display">
H = \frac{响应}{激励}</script><ul>
<li><p>若响应与激励在同一端口，则属策动点(driving point)函数；若响应与激励不在同一端口，则属转移(transfer)函数。</p>
<p>​    <img src="https://gitee.com/xqyr/img/raw/img/20220927162457.png" alt="分类"></p>
</li>
</ul>
</li>
</ul>
<h4 id="叠加原理"><a href="#叠加原理" class="headerlink" title="叠加原理"></a>叠加原理</h4><p><img src="https://gitee.com/xqyr/img/raw/img/20220927162741.png" alt="叠加"></p>
<script type="math/tex; mode=display">
i_2=H_1u_S + H_2i_s</script><ul>
<li>作为电路的响应y(t),与电路各个激励x(t)的关系可表示为：</li>
</ul>
<script type="math/tex; mode=display">
y(t)= \sum _{M}H_{m}x_{m}(t)</script><h4 id="叠加方法与功率计算"><a href="#叠加方法与功率计算" class="headerlink" title="叠加方法与功率计算"></a>叠加方法与功率计算</h4><ul>
<li>电源对电路提供的总功率等于<strong>电压源单独作用时对电路提供的功率</strong>和<strong>电流源单独作用时对电路提供功率</strong>的总和</li>
</ul>
<h3 id="第四章-分解法和单口网络-p-112"><a href="#第四章-分解法和单口网络-p-112" class="headerlink" title="第四章 分解法和单口网络 p_112"></a>第四章 分解法和单口网络 <em>p_112</em></h3><h4 id="分解法"><a href="#分解法" class="headerlink" title="分解法"></a>分解法</h4><ol>
<li>把给定网络划分为两个单口网络N1和N2 ;</li>
<li>分别求出N1和N2,的VCR（计算或测量）；</li>
<li>联立两者的VCR或由它们伏安特性曲线的交点，求得N1,和N2的端口电压、电流：</li>
<li>分别求解N1和N2内部各支路电压、电流。</li>
</ol>
<h4 id="单口网络的电压电流关系"><a href="#单口网络的电压电流关系" class="headerlink" title="单口网络的电压电流关系"></a>单口网络的电压电流关系</h4><ul>
<li>外施电流源求电压法和外施电压源求电流法是常用的方法，也是用实验方法确定VCR的依据</li>
</ul>
<blockquote>
<p>列题4-2 p116</p>
</blockquote>
<h4 id="置换定理"><a href="#置换定理" class="headerlink" title="置换定理"></a>置换定理</h4><p>若网络N出两个单口网络N1,和N2连接组成且己知端口电乐和电流值分别为α和β,则N2(或N1)可以用一个电压为a的电压源[或用一个电流为β的电流源置换，不影响N,(或N2)内各支路电压、电流原有数值。</p>
<p><img src="https://gitee.com/xqyr/img/raw/img/20220927172729.png" alt="置换定理"></p>
<h4 id="等效电路"><a href="#等效电路" class="headerlink" title="等效电路"></a>等效电路</h4><ul>
<li><p>如果一个单口网络N和另一个单口网络N’的电压、电流关系完全相同，亦即它们在“~i平面上的伏安特性曲线完全重在，则这两单口网络便是等效的。尽管这两个网络可以具有完全不同的结构，但对任一外电路M来说，它们却具有完全相同的影响，没有丝毫差别 。</p>
<p>​    <img src="https://gitee.com/xqyr/img/raw/img/20220927173103.png" alt="等效串联电路"></p>
</li>
</ul>
<h4 id="一些简单的等效电路"><a href="#一些简单的等效电路" class="headerlink" title="一些简单的等效电路"></a>一些简单的等效电路</h4><ul>
<li>(11)电压源与电阻的串联（戴维南）</li>
<li>(12)电流源与电阻的并联 （诺顿）</li>
</ul>
<p><img src="https://gitee.com/xqyr/img/raw/img/20220927174024.png" alt></p>
<script type="math/tex; mode=display">
\begin{matrix}
(a) \quad
u =u_s -Ri\\
(b) \quad
i = i_s - \frac u{R^`} \quad / \quad u=R^`i_s - R^`i\\
当R=R^`并且 U_S = R^`i_s（i_s=\frac {u_s}{R^`}）等效
\end{matrix}</script><h4 id="戴维南定理"><a href="#戴维南定理" class="headerlink" title="戴维南定理"></a>戴维南定理</h4><ul>
<li>含电源和线性电阻、受控源的单口网络（今后简称为含源线性单口网络）就其端口来说，可等效为<em>一个<u>电压源串联电阻支路</u></em>。电压源的电压等于该网络N的<strong>开路电压Uoc</strong>;串联电阻R等于该网络中所<strong>有独立源为零值</strong>时所得网络N的等效电阻R。</li>
</ul>
<h4 id="诺顿定理"><a href="#诺顿定理" class="headerlink" title="诺顿定理"></a>诺顿定理</h4><p>含源线性单口网络N,就其端口来看，可以等效为一个<em><u>电流源并联电阻组合</u></em>。电流源的电流等于该网络N的<strong>短路电流</strong>isc;并联电导G,等于该网络中所有<strong>独立源为零值</strong>时所得网络N。的等效电导Gb。这就是诺顿定理。这-电流源并联电导组合称为诺顿等效电路。</p>
<h4 id="最大功率传递定理"><a href="#最大功率传递定理" class="headerlink" title="最大功率传递定理"></a>最大功率传递定理</h4><p>的功率为最大的条件是：负载R应与戴维南（或诺顿）<strong><u>等效电阻相等</u></strong>。此即最大功率传递定理。，称为最大功率匹配此时负载得到的最大功率为</p>
<script type="math/tex; mode=display">
P_{max} = \frac {u_{oc}^2}{4R_o}</script><h3 id><a href="#" class="headerlink" title=" "></a> </h3>
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